System And Method For Determining The Current Focal Length Of A Zoomable Camera

ABSTRACT

An accurate camera pose is determined by pairing a first camera with a second camera in proximity to one another, and by developing a known spatial relationship between them. An image from the first camera and an image from the second camera are analyzed to determine corresponding features in both images, and a relative homography is calculated from these corresponding features. A relative parameter, such as a focal length or an extrinsic parameter is used to calculate a first camera&#39;s parameter based on a second camera&#39;s parameter and the relative homography.

FIELD OF THE INVENTION

The exemplary embodiments relate to systems and methods for determiningthe focal length of a first camera based on the focal length of a secondcamera positioned in proximity to the first camera.

BACKGROUND INFORMATION

An accurate camera pose is essential information in many systems, forexample, in camera systems intended to broadcast sporting events atstadiums. Some elements of a camera pose (e.g., pan, tilt, roll,position) are sometimes known, fixed, or obtainable with inexpensivesensors. Pan means translation; roll means rotation. The current orinstantaneous focal length of a zoomable camera is less frequentlyavailable, or of insufficient precision for many applications. Incameras that make their current focal length externally available, theresolution and/or absolute accuracy of the data may be too low for theapplication that requires focal length data. Thus, using a zoomablecamera that outputs its focal length has proven to be unreliable andproblematic.

In some cases, a portion or an entirety of the elements of a firstcamera pose can be determined by comparing the current view of the firstcamera with one or more static images or models of a scene, possiblyderived from cameras beforehand. In some other cases, a portion orentirety of the elements of a first camera pose can be determined bycomparing the current view of the first camera with concurrent imagesfrom one or more additional cameras, some of whose parameters are known.The extrinsic parameters of a camera include pan, roll, tilt, cameraposition, etc. This technique can be more useful than basing thedetermination on predetermined static images or scene models, since itcan adapt to changes in lighting or background.

Many systems rely upon visual recognition of pre-determined scenes tosolve for focal length (and other camera parameters). However, when thecurrent scene is not a pre-determined, expected scene, a camera pose isnot calculable. This may also occur when the camera is pointed away froma pre-determined scene (for instance, pointing at the audience), or whenthe camera is zoomed so far in or out that either expected fiducials aretoo few in number, or so small that they are unusable, or are occludedby foreground objects.

Typically, positions of landmarks in the scene are represented by a 3DModel. At intermediate zoom levels, the landmark position points of themodel may be matched with their corresponding feature points from thecurrent video image. Based on these pairs of corresponding points ahomography (projective mapping between planar points from a 3D space andtheir projection in the image space) is calculated. Then, cameraparameters are estimated based on the calculated homography.Pre-determined landmarks imply the need for a scene model. This is ofteninconvenient, or impossible. Nevertheless, a relative homography (or thehomography) may be established between zoom-invariant, but ad-hocfeature points in simultaneous views of the same scene from two cameras.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram of a system for determining the focallength of a zoomable camera.

FIG. 2 shows a functional block diagram illustrating a focal lengthcalculating arrangement for calculating the focal length of a firstcamera.

FIG. 3 is a flow diagram illustrating the method for determining theabsolute focal length of the first camera 105.

DETAILED DESCRIPTION

The exemplary embodiments may be further understood with reference tothe following description of the exemplary embodiments and the relatedappended drawings, wherein like elements are provided with the samereference numerals. The exemplary embodiments are related to systems andmethods for detecting objects in a video image sequence. The exemplaryembodiments are described in relation to the detection of players in asporting event performing on a playing surface, but the presentinvention encompasses as well systems and methods where determination ofa camera focal length is required for accurate and visually desirableimaging of a static or dynamic scene. The exemplary embodiments may beadvantageously implemented using one or more computer programs executingon a computer system having a processor or central processing unit, suchas, for example, a computer using an Intel-based CPU, such as a Pentiumor Celeron, running an operating system such as the WINDOWS or LINUXoperating systems, having a memory, such as, for example, a hard drive,RAM, ROM, a compact disc, magneto-optical storage device, and/or fixedor removable media, and having a one or more user interface devices,such as, for example, computer terminals, personal computers, laptopcomputers, and/or handheld devices, with an input means, such as, forexample, a keyboard, mouse, pointing device, and/or microphone.

An exemplary embodiment proposes to use a pair of cameras positioned inproximity to each other and with a known spatial mapping between theiroptical axes. This spatial mapping may be derived from the relativehomography, as will be explained in detail below. The relativehomography calculation is based on corresponding feature pairs, wherecorrespondence is between a first camera's image projection and a secondcamera's image projection of the same landmark from the scene. Anabsolute homography computation is based on corresponding feature pairs,where correspondence is between a landmark at the scene model (e.g.landmark's real-world position) and its projection in the camera image.Although the embodiment is described in connection with one widefield-of-view camera (the second camera), there may be associated withthe zoomable camera more than one WFOV camera. Although the preferredembodiment is discussed within the context of these cameras being usedfor coverage of a sporting event, it is to be understood that theexemplary embodiments are applicable to other contexts, such as, forexample virtual world applications like augmented reality, virtualstudio applications, etc. In the sports coverage example, the firstcamera tends to zoom in and out frequently, so that there may be largediscrepancies in focal length between the first and second cameras.Matching corresponding features from two images with large differencesin scale may be challenging. In addition to the discrepancy in scale,the problem may be complicated by the number and types of features thatare to be reliably extracted and matched at a certain camera view. Inthe preferred embodiment, the first camera is a zoom-able camera, whilethe second camera has a fixed focal length and is set to capture a widefield-of-view of the scene. The first and second cameras shareapproximate pan, tilt, roll, and position pose elements, but not focallength. The focal length of the first camera may be calculated from 1)the known focal length of the second camera and 2) the relativehomography between the first and second cameras generated fromcorresponding features extracted from images taken by these two cameras.

The features that may be used in the homography calculation include, forexample, key-points, lines, and conics. These geometrical features areinvariant under projective mapping (for example a conic projectivelymaps to a second corresponding conic). Note that in order to establishcorrespondence between two geometrical features, various image analysismethods may be employed, such as computing metrics based on the textureor color statistics of local pixels. In this disclosure, a combinationof extractable key-points, lines, and conics, is utilized to solve forthe homography via a linear equation system as explained in furtherdetail below.

FIG. 1 is a schematic diagram of a system 100 for determining the focallength of a zoomable camera. In FIG. 1, first camera 105 is zoomable,and second camera 110 is not, having instead a fixed focal length andset to a field of view wide enough to capture enough fiducials to enablea calculation of a homography based on common geometric features betweenthe images of the cameras 105, 110 (described below). Cameras 105, 110may be attached to one another, through a mechanical connection 130,such that translations and rotations experienced by the first camera 105are duplicated simultaneously in the second camera 110, and aligned suchthat the optical axes 115, 120 of cameras 105, 110 are parallel (asillustrated in FIG. 1), or are arranged according to some other relativeorientation to one another that is known. Alternatively, cameras 105,110 need not be physically attached to one another, so long as thespatial relation (or a rigid transformation) that maps one camera toanother is extractable. In this alternative, the cameras 105, 110 areapproximately co-located, but otherwise may be oriented differently aslong as cameras 105, 110 cover enough corresponding features tocalculate the homography. Note that, in the case where first camera andsecond camera are mechanically attached, due to vibrations or otherpractical reasons, there may still be a differential relativeorientation that should be accounted for (meaning to receive an accurateresult when calculating the first camera focal length, one should alsomodel possible discrepancies in relative panning, tilting, or rollingbetween the two cameras).

FIG. 2 shows a functional block diagram illustrating a focal lengthcalculating arrangement 200 for calculating the focal length of thefirst camera 105. In terms of a hardware implementation, the variousmodules illustrated collectively FIG. 2 may be embodied as a singleprocessing device, such as a suitable programmed microprocessor, or as asystem on a chip, ASIC, or any other programmable arrangement.Arrangement 200 may be housed inside either of cameras 105 or 110, or itmay be located remotely in a media truck at the sporting venue or abroadcast studio. In the case of a remotely located arrangement, 200,the various information on camera pose elements may be transmitted toarrangement 200 either wirelessly through any suitable transmissionmedium (RF, IR, ultrasonic), through a direct wired connection, througha network like an ETHERNET network, or through the Internet.

The image from first camera 105 and the image from second camera 110 aresupplied to a module 205 for determining the corresponding geometricfeatures of the two images. These corresponding features may include,for example, points, lines, and conics from both images. The extractionand matching between these corresponding features may be accomplishedaccording to any suitable method known in the art. For example, a knownin the art method such as SIFT (Scale-Invariant Feature Transformation)or SURF (Speeded Up Robust Feature) may be used.

The extracted corresponding features are supplied to a linear homographycalculating module 210. The particular technique for calculating thehomography depends on the particular category of common featureextracted from the images. For instance, known methods linearly estimatethe homography matrix based on corresponding set of points and/or lines.Some methods estimate the homography based on corresponding set ofconics. In practice, as the camera 105 steers and zooms in order tocover an action of an event, at times, the available projected features(key-points, lines, or conics) are sparse. Therefore, a robust (linear)method that estimates the homography out of any currently availablecombination of features is advantageous and described in detail below.

The homography calculating module 210 receives from module 205 acombination of corresponding pairs of points, lines, and/or conics fromtwo planar images from cameras 105, 110. As shown in the table below, apoint, a line, and a conic extracted from a first image I, whenundergoing projective mapping H_(3×3) onto image I′ preserve theirgeometric properties. Meaning a point, a line, and a conic are invariantunder the projective mapping (a point maps into a point, a line mapsinto a line, and a conic maps into a conic).

A Point A Line A Conic X′ = H · X l′ = H^(−T) · l C′ = H^(−T) C^(−T) ·H⁻¹ Where Where Where X = (x, y, 1)^(T); X ε I l = (a, b, c)^(T); l ε I${C = \begin{bmatrix}a & b & d \\b & c & e \\d & e & f\end{bmatrix}};{C \in I}$ X′ = (x′, y′, 1)^(T); X′ ε I′ l′ = (a, b,c)^(T); l′ ε I′ ${C^{\prime} = \begin{bmatrix}a^{\prime} & b^{\prime} & d^{\prime} \\b^{\prime} & c^{\prime} & e^{\prime} \\d^{\prime} & e^{\prime} & f^{\prime}\end{bmatrix}};{C^{\prime} \in I^{\prime}}$An estimate for the homography is determined by solving a homogeneousequation system: M·h=0, where h is a concatenation of H's rows:h^(T)≡[h₁₁,h₁₂,h₁₃,h₂₁,h₂₂,h₂₃,h₃₁,h₃₂,h₃₃] and M is derived from thegiven corresponding features in I and I′ as is explained below for thecases of corresponding 1) pair of points, 2) pair of lines, and 3) twopairs of conics.

With regard to homogenous equations from a pair of corresponding pointsX and X′, under projective mapping there exists X′=H·X. Employing thecross product of X′ on both sides of the equations yields: X′×X′=X′×H·X.Since by definition X′×X′=0, X′×H·X=0. The form X′×H·X=0 can be writtenas M·h=0 where M may be derived as follows:

$M \equiv \begin{bmatrix}0 & 0 & 0 & {{- X_{3}^{\prime}}X_{1}} & {{- X_{3}^{\prime}}X_{2}} & {{- X_{3}^{\prime}}X_{3}} & {X_{2}^{\prime}X_{1}} & {X_{2}^{\prime}X_{2}} & {X_{2}^{\prime}X_{3}} \\{X_{3}^{\prime}X_{1}} & {X_{3}^{\prime}X_{2}} & {X_{3}^{\prime}X_{3}} & 0 & 0 & 0 & {{- X_{1}^{\prime}}X_{1}} & {{- X_{1}^{\prime}}X_{2}} & {{- X_{1}^{\prime}}X_{3}} \\{{- X_{2}^{\prime}}X_{1}} & {{- X_{2}^{\prime}}X_{2}} & {{- X_{2}^{\prime}}X_{3}} & {X_{1}^{\prime}X_{1}} & {X_{1}^{\prime}X_{2}} & {X_{1}^{\prime}X_{3}} & 0 & 0 & 0\end{bmatrix}$

Note that only two equations are linearly independent.

With regard to homogenous equations derived from a pair of correspondinglines, l and l′, under projective mapping there exists l′=H^(−T)·l.Employing the cross product of l′ on both sides of the equation yields:l′×l′=l′×(H^(−T)·l). Since by definition l′×l′=0, l′×(H^(−T)·l)=0. Theform l′×(H^(−T)·l)=0 can be written as M·h=0, where M may be derived asfollows:

$\begin{matrix}{M \equiv \begin{bmatrix}0 & {{- l_{3}}l_{1}^{\prime}} & {l_{2}l_{1}^{\prime}} & 0 & {{- l_{3}}l_{2}^{\prime}} & {l_{2}l_{2}^{\prime}} & 0 & {{- l_{3}}l_{3}^{\prime}} & {l_{2}l_{3}^{\prime}} \\{l_{3}l_{1}^{\prime}} & 0 & {{- l_{1}}l_{1}^{\prime}} & {l_{3}l_{2}^{\prime}} & 0 & {{- l_{1}}l_{2}^{\prime}} & {l_{3}l_{3}^{\prime}} & 0 & {{- l_{1}}l_{3}^{\prime}} \\{{- l_{2}}l_{1}^{\prime}} & {l_{1}l_{1}^{\prime}} & 0 & {{- l_{2}}l_{2}^{\prime}} & {l_{1}l_{2}^{\prime}} & 0 & {{- l_{2}}l_{3}^{\prime}} & {l_{1}l_{3}^{\prime}} & 0\end{bmatrix}} & \;\end{matrix}$

Note that only two equations are linearly independent.

With regard to homogenous equations derived from two pairs ofcorresponding conics C₁, C₂ and C₁′, C₂′, and assuming non-degenerativeconics (i.e. determinant det(C)≠0) corresponding conics are related asfollows:

s ₁ ·C ₁ =H ^(T) C ₁ ′·H

s ₂ ·C ₂ =H ^(T) C ₂ ′·H

Computing the determinant, s_(i) ³·det(C_(i))=det(C_(i)′)·det(H)², andthen setting det(H)²=1 results in: s_(i)=(det(C_(i)′)/det(C_(i)))^(1/3).Hence, C_(i) and C_(i)′ are normalized so that det(C_(i))=det(C_(i)′).The normalized conics satisfy:

C ₁ =H ^(T) ·C ₁ ′·H

C ₂ =H ^(T) ·C ₂ ′·H

Multiplying the inverse of first equation with the second equationresults:

C ₁ ⁻¹ ·C ₂ =H ⁻¹ ·C ₁′⁻¹ ·C ₂ ′·H

And then multiplying both sides by H yields a linear system with respectto the element of H:

C ₁′⁻¹ ·C ₂ ′·H−H·C ₁ ⁻¹ ·C ₂=0

Or

A·H−H·B≡M·h=0

Where, M may be derived as follows:

${M \equiv \begin{bmatrix}M_{11} & M_{12} & M_{13} & A_{12} & A_{12} & A_{12} & A_{13} & A_{13} & A_{13} \\A_{21} & A_{21} & A_{21} & M_{24} & M_{25} & M_{26} & A_{23} & A_{23} & A_{23} \\A_{31} & A_{31} & A_{31} & A_{32} & A_{32} & A_{32} & M_{37} & M_{38} & M_{39}\end{bmatrix}},$

and where,

-   M₁₁=A₁₁−B₁₁−B₁₂−B₁₃, M₁₂=A₁₁−B₂₁−B₂₂−B₂₃, M₁₃=A₁₁−B₃₁−B₃₂−B₃₃,    M₂₄=A₂₂−B₁₁−B₁₂−B₁₃, M₂₅=A₂₂−B₂₁−B₂₂−B₂₃, M₂₆=A₂₂−B₃₁−B₃₂−B₃₃,    M₃₇=A₃₃−B₁₁−B₁₂−B₁₃, M₃₈=A₃₃−B₂₁−B₂₂−B₂₃, and M₃₉=A₃₃−B₃₁−B₃₂−B₃₃.    In this case, all three equations are linearly independent.

The following shall discuss determining minimum features for a uniquesolution (up to a scale) for the system M·h=0. In order to determine aunique solution, the rank of M should be eight, meaning the number ofindependent equations should be at least 8. Since a pair ofcorresponding points results in two independent equations, a pair ofcorresponding lines results in two independent equations, and two pairsof corresponding conics result in three independent equations, anycombination of corresponding lines, points, and conics that result in atleast 8 linear equations will be sufficient for the computation of h(except for the combination of two lines and two points). Therefore,many possible combinations of corresponding features from the pair ofimages for satisfying the eight linear equation are possible. Forinstance, one pair of points (one from each image), together with threepairs of corresponding lines (or vice versa) would produce eightindependent equations. Similarly, two pairs of corresponding points, onepair of corresponding lines, and two pairs of corresponding conics(yielding three equations) would produce nine available independentequations. Determining such combinations of eight equations is done foreach frame of the images from cameras 105 and 110. Thus, for a firstpair of frames from the cameras, the eight equations may consist ofequations from a pair of corresponding points in the first pair ofimages and equations from three pairs of corresponding lines in thefirst pair of images. For the next pair of frames, the eight equationsmay be determined from a different combination of correspondingfeatures. In the case where accurate relative spatial orientationbetween the two cameras is given (or, for example, a subset of theparameters: relative pan, relative tilt, and relative roll is given),fewer corresponding feature pairs (i.e. fewer independent equations) areneeded to solve for the first camera focal length. For example, when therelative orientation is fully known, two pairs of corresponding featuresare sufficient to calculate the relative focal length.

Once a unique solution is determined for the relative homography of aconcurrent pair of frames of the two camera images, the absolute focallength of the first camera 105 can be determined. Specifically, once therelative homography for the current frames of the images from cameras105, 110 is determined, it will contain the relative focal lengthbetween the two cameras 105, 110. That is, the relative focal lengthtaken from the relative homography is the ratio of the apparent focallength of the first camera 105 with the known focal length of the secondcamera 110. Once this ratio is known, the absolute focal length of thefirst camera 105 is determined by multiplying the ratio by the absolutefocal length of the second camera 110.

FIG. 3 is a flow diagram illustrating the method for determining theabsolute focal length of the first camera 105. Step 300 involvesreceiving a current frame of a first image from camera 105 and a currentframe of a second image from second camera 110. In step 305,corresponding geometrical features from the current frames aredetermined. As explained above, combinations of corresponding points,lines, and conics are determined continually to generate, for thegeneral case, at least eight independent equations. Once the equationsare determined, they are used in Step 310 to compute a unique solutionfor the relative homography H. The relative homography includes therelative focal length between the cameras 105, 110. The homographyprovides the ratio of focal lengths, that is, the relative focal length.Once the relative focal length is known, it is multiplied by the knownfocal length of camera 110 to determine the absolute focal length ofcamera 105. The method has been described as a single instance of focallength determination, but this method can be repeated as often as isneeded. For instance, the focal length calculation can be performed forevery frame of the images produced by cameras 105, 110, every otherframe, or as often or as infrequently as the particular applicationrequires. For instance, in an application requiring frequent changes ofthe focal length of camera 105, the exemplary embodiments can be keeptrack of the focal length changes by calculating the focal length on aperiodic basis, with the period between calculations being determinedaccording to the necessities of the particular application.

The exemplary embodiments can work with any camera/lens withoutmodification. Moreover, the exemplary embodiments achieve the purpose ofdetermining a focal length for a first camera that is attached to asecond camera even if the observed scene does not match a known model.This situation may result if the observed scene contains too few, or no,known fiducials. In some applications, some or all of pan, tilt, roll,and position may be fixed, known, or available from sensors. Theaddition of current focal length according to the exemplary embodimentscan provide a full camera pose, without recourse to visualmodel-matching. The exemplary embodiments can enable a model-matchingsystem to determine a full first camera pose, even if the first cameracannot view enough fiducials to form a model. If the second camera'sfield of view is set to a wide-enough field of view to capture enoughfiducials to form a model, the second camera model will determinetranslation and rotation which is shared by the first camera (since theymay be attached). Then, the first camera's calculated focal length issubstituted for the second camera's focal length. With regard to thelinear computation of the homography from any available combination ofcorresponding keypoints, lines, and/or conics (e.g., common features ina game arena), once the homography is known the camera model may beestimated based on methods known in the prior art.

Typically, the second camera is set to capture a wide view of the scene,and, relative to the first camera, may be steered slowly without rapidchanges in orientation and zoom level. Thus, second camera's parametersmay be derived based on a known model of the scene, for example, thepoints (e.g. line intersections), lines and circles that constitute aHockey rink. Due to the camera wide view, a combination of points,lines, and circles from the rink are likely to be concurrently capturedwithin a video frame forming corresponding pairs (e.g. a line from thescene model of the rink corresponds to its projection in the videoframe). Out of these corresponding pairs, an absolute homography may becalculated following the method described above for the relativehomography. Out of this absolute homography, the second camera'sparameter may be calculated following methods in the art.

What is claimed is:
 1. A method, comprising: receiving a first imagefrom a first camera; receiving a second image from a second camera,wherein the second camera is positioned with a relative orientation tothe first camera; receiving a camera parameter of the second camera;determining a first set of corresponding feature pairs common to thefirst image and the second image; determining, based on the first set ofcorresponding feature pairs, a relative homography between the firstimage and the second image; and calculating a camera parameter of thefirst camera based on the relative homography and the camera parameterof second camera.
 2. The method of claim 1, wherein the camera parameterof the second camera is a focal length and calculating the cameraparameter of the first camera includes calculating the focal length ofthe first camera.
 3. The method of claim 1, wherein the camera parameterof the second camera is an extrinsic parameter and calculating thecamera parameter of the first camera includes calculating an extrinsicparameter of the first camera.
 4. The method of claim 1, wherein thefirst set of corresponding feature pairs includes one of a set of commonpoints, a set of common lines, a set of common conics, and a combinationinvolving two or more of a set of common points, a set of common lines,and a set of common conics.
 5. The method of claim 1, wherein the cameraparameter of the second camera is computed based on: determining asecond set of corresponding feature pairs common to the second image anda scene model; determining, based on the second set of correspondingfeature pairs, an absolute homography between the second image and thescene model; and calculating the camera parameter of the second camerabased on the absolute homography between the second image and the scenemodel.
 6. The method of claim 5, wherein the second set of correspondingfeature pairs includes one of a set of common points, a set of commonlines, a set of common conics, and a combination involving two or moreof a set of common points, a set of common lines, and a set of commonconics.
 7. A system, comprising: a geometric feature determining modulefor receiving a first image from a first camera and for receiving asecond image from a second camera, wherein the second camera ispositioned with a relative orientation to the first camera, thegeometric feature determining module receiving a camera parameter of thesecond camera and determining a first set of corresponding feature pairscommon to the first image and the second image; a homography determiningmodule for determining, based on the first set of corresponding featurepairs, a relative homography between the first image and the secondimage; and a calculation module for calculating a camera parameter ofthe first camera based on the relative homography and the cameraparameter of second camera.
 8. The system of claim 7, wherein the cameraparameter of the second camera is a focal length and the calculating ofthe camera parameter of the first camera by the calculation moduleincludes calculating the focal length of the first camera.
 9. The systemof claim 7, wherein the camera parameter of the second camera is anextrinsic parameter and the calculating of the camera parameter of thefirst camera by the calculation module includes calculating an extrinsicparameter of the first camera.
 10. The system of claim 7, wherein thefirst set of corresponding feature pairs includes one of a set of commonpoints, a set of common lines, a set of common conics, and a combinationinvolving two or more of a set of common points, a set of common lines,and a set of common conics.
 11. The system of claim 7, wherein thecamera parameter of the second camera is computed based on: determininga second set of corresponding feature pairs common to the second imageand a scene model; determining, based on the second set of correspondingfeature pairs, an absolute homography between the second image and thescene model; and calculating the camera parameter of the second camerabased on the absolute homography between the second image and the scenemodel.
 12. The system of claim 11, wherein the second set ofcorresponding feature pairs includes one of a set of common points, aset of common lines, a set of common conics, and a combination involvingtwo or more of a set of common points, a set of common lines, and a setof common conics.
 13. A computer-readable medium containing instructionsthat when executed on a computing device results in a performance of thefollowing: receiving a first image from a first camera; receiving asecond image from a second camera, wherein the second camera ispositioned with a relative orientation to the first camera; receiving acamera parameter of the second camera. determining a first set ofcorresponding feature pairs common to the first image and the secondimage; determining, based on the first set of corresponding featurepairs, a relative homography between the first image and the secondimage; and calculating a camera parameter of the first camera based onthe relative homography and the camera parameter of second camera. 14.The computer-readable medium of claim 13, wherein the camera parameterof the second camera is a focal length and calculating the cameraparameter of the first camera includes calculating the focal length ofthe first camera.
 15. The computer-readable medium of claim 13, whereinthe camera parameter of the second camera is an extrinsic parameter andcalculating the camera parameter of the first camera includescalculating an extrinsic parameter of the first camera.
 16. Thecomputer-readable medium of claim 13, wherein the first set ofcorresponding feature pairs includes one of a set of common points, aset of common lines, a set of common conics, and a combination involvingtwo or more of a set of common points, a set of common lines, and a setof common conics.
 17. The computer-readable medium of claim 13, whereinthe camera parameter of the second camera is computed based on:determining a second set of corresponding feature pairs common to thesecond image and a scene model; determining, based on the second set ofcorresponding feature pairs, an absolute homography between the secondimage and the scene model; and calculating the camera parameter of thesecond camera based on the absolute homography between the second imageand the scene model.
 18. The computer-readable medium of claim 17,wherein the second set of corresponding feature pairs includes one of aset of common points, a set of common lines, a set of common conics, anda combination involving two or more of a set of common points, a set ofcommon lines, and a set of common conics.